First of all, you have to use the following link from your smartphone to have the locations of the different places I mention in google maps.
https://drive.google.com/open?id=1i81Ilk_fNMcniIFAeIcvKK-j2_C7KLJ_&usp=sharing
I've tried to select in addition to the "normal" places to visit, some additional places (and of course the foodie side). And for sure you are going to visit the 2.DUOMO, 3.SIGNORIA, 4.ACADÈMIA (where Michel Angelo's David is), 5. UFIZZI, etc. you'll find everywhere a lot of info of these places).
Let's start with the interesting places. The first part is for your first hour there, the rest, to improvise whenever you like:
If you've just arrived my suggestion is: leave your luggage, breath for a moment, and simply go for a walk around the Duomo, with the lights on it will give to you an unforgettable impression... if possible sit there, order a wine, and enyoy your first moments in the city
If you need more, you can walk (only 400m.) to the 3.PIAZZA DELLA SIGNORIA, but don't be tempted to see the whole city that night, you will have plenty of time!!
6. CHIESA e MUSEO DI ORSANMICHELE one of the most beautiful churches in Firenze, with a wonderful facade, only 100m from 3.SIGNORIA
7. PONTE VECCHIO one of the symbols of the city, over the river Arno. The best views are from the PONTE SANTA TRINITA (next bridge going West) or even the next PONTE ALLA CARRAIA... The best of these two bridges is that in the south end, you can find two of the best ice cream shops in Firenze: 9. GELATERIA SANTA TRINITA and 8. GELATERIA LA CARRAIA (the latter used to be less expensive and had more italian clients).
One option is go to the 10.HOTEL LUNGARNO to take some photos from the 7.PONTE VECCHIO and PONTE SANTA TRINITA. This hotel has an open-access terrace (you don't need to order anything if you don't want to, a lot of tourists go there to take photos)
27.CONTINENTALE SKY LOUNGE. Also a nice terrace to have a cocktail (not cheap) with views of the river, 7.PONTE VECCHIO, but also the roofs, 3.LA SIGNORIA, etc. I am not sure if you can access without a reservation.
11.CAFFETTERIA DELLE OBLATE. It's time to have an informal Aperitivo with amazing views of the roofs, including Duomo's Dome, this is the Cafeteria of the Oblate Nuns Library (it is no longer a convent). The terrace is located on the upper flor. You pay a fixed fee and for that you will have a drink and serve yourself from the different Aperitivo meals prepared. Normally there is a lot of food but the main reason to go there is the sensation that you are touching the Dome! (it is really huge).
20. CAPPELLE MEDICEE. Built by the famous family (as a lot of other monuments and buildings there). You have to visit it...and tell me what do you think of it.
23. SAN MARCO MUSEUM. Most people don't visit it, but trust me, you should. It's a church and convent built by the Medicci for the Dominican friars. In the area of the Dormitories, with the simple cells of the monks is on the upper floor. when you're going up if you take a look at the wall of the cells then you will find the wonderful fresco of Fra Angelico: Annunciation... I couldn't believe it was there in front of me...and the amazing colours... There are frescos of Fra Angelico everywhere... the contrast between the austerity of the cells and the wonder of the paintings is amazing.
24. BARGELLO MUSEUM. With paintings of Tuscan authors including several from Michelangelo... is in the Palazzo del Bargello a nice building. Not as relevant as Uffizi
25. ARCHAELOGICAL MUSEUM. For me it's worth visiting , only to see the "Quimera de Arezzo" but there are also other interesting things.
26. PALAZZO PITTI and the BOBOLI GARDENS. A Renascentist Palace with wonderful rooms. Don't miss it with time to walk through the Boboli Gardens...
12. SAN MINIATO AL MONTE. The older and for most people the most beautiful church (...of course, everything in Firenze is the "most" beautiful..). During the sunset the views from the open space in front of the church overlooking Firenze's landscape are something to remember. If you want to visit the church take a look at the closing time before, may close early. To get there, the best is to get on the bus from 13.SANTA MARIA NOVELLA STATION. lines #12 and #13
14. PROFUMO FARMACEUTICO SANTA MARIA NOVELLA Next to BASILICA DI SANTA MARIA NOVELLA. Is a very old pharmacy transformed in a mix of museum and shop (the continue to produce and sell cosmetics, teas and others). You can buy some tea or only walk through the old rooms with glass devices and tools perfectly conserved. It'll took you not too much and for me was interesting.
From the other side of the city, North of the city center, you can find the hills of Firenze, Via Bolognese. From the 15.GIARDINO DE L'ORTICULTURA you will have views of the city from the other perspective.
¡¡¡¡ ANOTHER FOODIE MOMENT !!!! These area is plenty of restaurants, but I prefer to suggest you the more authentic places, usually visited by italian people:
16. LE MURATE CAFFÈ LETTERARIO. Good italian food and cultural atmosphere
17. OSTERIA DE' PAZZI. Traditional Tuscan Osteria
18. BOCCADAMA. in Piazza di Santa Croce. Also Tuscan food. The place is perfect. Go to have dinner. You have to book a table outside looking at the facade of the Basilica di Santa Croce. If you like take a book and enjoy your time after dinner, or simply finish your wine while enjoying the views.
19. VICO DEL CARMINE. Nothing special but very good napolitan food. Pizza Napolitana, but also bistecca alla fiorentina (if you like meat -a lot of meat-, bisteca fiorentina is a beef cut 1kg.aprox of the rib cage and loin in the same cut... (only to share!!!)
21. CIBREO RESTAURANT. Is the restaurant of one of the most famous chefs in Firenze: Fabio Picchi, the soups are famous, the food is top level (but also the prices).
22. OSTERIA DA QUE GANZI. A good lunch menu in a quiet place.
28. LA GIOSTRA. Nice decoration and local food.
And now, if you have the opportunity to visit other villages in Tuscany, they're all beutiful, It is impossible to visit all of them, these are several villages I've visited, but take a look in the internet, decide which your trips and enjoy:
https://drive.google.com/open?id=1YKGGx3Rsa-bItg78SJygCx0Gx70e6O8C&usp=sharing